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Intuitionistic Fuzzy Stability of Functional Equations Associated with Inner Product Spaces

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  • Zhihua Wang
  • Themistocles M. Rassias

Abstract

In intuitionistic fuzzy normed spaces, we investigate some stability results for the functional equation ∑i=1nf(xi-(1/n)∑j=1nxj)=∑i=1nf(xi)-nf((1/n)∑i=1nxi) which is said to be a functional equation associated with inner products space.

Suggested Citation

  • Zhihua Wang & Themistocles M. Rassias, 2011. "Intuitionistic Fuzzy Stability of Functional Equations Associated with Inner Product Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:456182
    DOI: 10.1155/2011/456182
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    References listed on IDEAS

    as
    1. Mohiuddine, S.A., 2009. "Stability of Jensen functional equation in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2989-2996.
    2. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    3. Mursaleen, M. & Mohiuddine, S.A., 2009. "Nonlinear operators between intuitionistic fuzzy normed spaces and Fréchet derivative," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1010-1015.
    4. Soon-Mo Jung, 2011. "Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4419-9637-4, April.
    5. M. Mursaleen & V. Karakaya & S. A. Mohiuddine, 2010. "Schauder Basis, Separability, and Approximation Property in Intuitionistic Fuzzy Normed Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    6. Mohiuddine, S.A. & Danish Lohani, Q.M., 2009. "On generalized statistical convergence in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1731-1737.
    7. Mursaleen, M. & Mohiuddine, S.A., 2009. "Statistical convergence of double sequences in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2414-2421.
    8. Choonkil Park & Won-Gil Park & Abbas Najati, 2009. "Functional Equations Related to Inner Product Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    9. Mursaleen, M. & Mohiuddine, S.A., 2009. "On stability of a cubic functional equation in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2997-3005.
    10. M. Mursaleen & V. Karakaya & S. A. Mohiuddine, 2010. "Schauder Basis, Separability, and Approximation Property in Intuitionistic Fuzzy Normed Space," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-14, January.
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